This is an announcement for the paper "The complex Busemann-Petty problem for arbitrary measures" by Marisa Zymonopoulou. Abstract: The complex Busemann-Petty problem asks whether origin symmetric convex bodies in C^n with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n\leq 3 and negative if n\geq 4. In this article we show that the answer remains the same if the volume is replaced by an "almost" arbitrary measure. This result is the complex analogue of Zvavitch's generalization to arbitrary measures of the original real Busemann-Petty problem. Archive classification: math.FA The source file(s), CBPGM.tex: 37275 bytes, is(are) stored in gzipped form as 0807.0779.gz with size 10kb. The corresponding postcript file has gzipped size 89kb. Submitted from: marisa@math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.0779 or http://arXiv.org/abs/0807.0779 or by email in unzipped form by transmitting an empty message with subject line uget 0807.0779 or in gzipped form by using subject line get 0807.0779 to: math@arXiv.org.